Ring location

ABSTRACT

The invention concerns a method for locating, in a digital image, a circle centre comprising the following steps: a) predefining a set of potential radii of the circle; b) dimensioning ( 303 ) two accumulators to a dimension in the form of a column matrix not larger than the size of the image in x-axis and a line matrix not larger than the size of the image in y-axis; c) sequentially, for each pixel image of the image: (i) selecting successively each potential radius; (ii) evaluating the position of the potential center of a circle of the selected radius and whereof the pixel concerned is on the periphery; and (iii) incrementing accumulators at the x-axis and the y axis of the potential center; and d) selecting ( 304 ) as coordinates of the located centre, the x-axis and the y-axis corresponding to the maximum of accumulators.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to the localization, in a digitized image,of a ring-shaped surface included between two substantially concentricgeometric shapes of generally circular shape. More specifically, thepresent invention relates to the detecting of a ring extending betweentwo circles of different radiuses, the circle having the smaller radiusbeing strictly included in the circle of greater radius.

2. Discussion of the Related Art

An example of application of the present invention is the localizationof the iris of an eye in a digitized image. Indeed, an eye may becharacterized as being an assembly of substantially concentric ellipticgeometric shapes: the eyebrows define a contour that is followed byeyelashes, which surround the eye ground, which includes a substantiallycircular iris containing a substantially circular pupil. In such anapproximately concentric pattern, the position of the centers andradiuses of the two circular patterns of the pupil and of the iris isdesired to be extracted, to extract from the image the ring forming theiris. For clarity, it is considered in the following description thatthe limits of the pupil and of the iris are perfect circles.

FIG. 1 illustrates, in a flowchart, an example of a known method forlocalizing an iris of an eye. FIGS. 2A to 2C illustrate the digitalimage which is the object of the method at different steps of theimplementation thereof.

Such a method starts with a step 101 (ACQUIRING EYE IMAGE) in which adigital image of an eye is acquired. The eye is digitized so that theobtained image is full size (scale 1:1). Such an image may be obtainedby any biometry terminal enabling capturing an eye image. For example,the acquisition is performed by a CCD digital camera of a 580×760-pixelimage, in black and white by infrared illumination, the eye being placedat a few centimeters only of the camera.

Localizing an iris in such an image then consists of localizing thecenter and the radius of the pupil as well as the center and the radiusof the iris. Indeed, although the pupil is strictly included in theiris, its is generally slightly off-centered with respect thereto.

A known method for determining the centers of the pupil and of the irisand their radiuses is based on the following observation. In infraredillumination, on the one hand, the iris contrasts on the white of theeye. On the other hand, the contour of the pupil contrasts with respectto the peripheral iris. This contrast translates on the digital image asvery different levels of grey on either side of the limit between theiris and the cornea, on the one hand, and of the limit between the irisand the pupil, on the other hand. The gradient, in terms of levels ofgrey, of the points located on the iris or pupil contour is then veryhigh. Generally, the contrast between the pupil and the iris is greaterthan the contrast between the iris and the cornea.

Localizing the iris consists of successively considering each point inthe image as the possible center and of measuring the gradients of thepoints located on arcs of a circle centered on the considered possiblecenter. The radiuses of these arcs of a circle vary within a range ofpossible radiuses of a pupil or of an iris at the considereddigitization scale. For a 580×760-pixel image at scale 1:1, the pupildiameter is considered to range between 30 and 100 pixels, and the irisdiameter is considered to range between 100 and 180 pixels. The centerof the pupil or of the iris then is the point for which, in the radiusrange corresponding to the pupil, respectively, to the iris, thegradient variation is the most significant. The gradient variationcalculations are performed by means of integro-differential operators.

To reduce the amount of calculation and the processing time, theintegro-differential operators are applied, at step 102 (LOCATING IRIS)which follows acquisition 101, to successive grids of pointsrepresenting possible centers. The successive grids have decreasingdimensions and pitches. Thus, in a first iteration 103 (i=0, s=s₀), itis for example chosen to apply on the digitized image illustrated inFIG. 2A a first grid of dimensions close to those of the image and of arelatively large first pitch s₀, for example, s₀=25 pixels, that is,including a possible center every 25 pixels in both directions. Further,the centers of the iris and of the pupil being confounded or slightlyoff-centered, the center and contour of the sole pupil are firstlocalized by applying the operators on arcs of a circle having diametersvarying from 30 to 100 pixels.

At the next iteration i=1, the grid pitch is reduced to refine thecenter determination. This pitch reduction goes along with a reductionof the grid dimensions and a centering thereof in the region of highestgradient variations. As illustrated in FIG. 2B, it is considered, forexample, that for second iteration i=1, pitch s₁ is 10 pixels. If thenumber of points in the grid is constant, its size reduction isautomatic with the pitch reduction.

Again, the integro-differential operators are applied for each point inthe grid and the existence of a center or of a region in which, forseveral points, the gradient variation (levels of grey) is the strongestis detected.

For each iteration i and each corresponding pitch s_(i), the process isthus repeated by applying in a block 104 (INTEGRO-DIFFERENTIAL OPERATOR)the integro-differential operators on grids of decreasing pitch s_(i)and of more and more reduced dimensions.

After each passing through block 104, a possible center and radius areobtained for the pupil at block 105 (CENTER & RADIUS), which areincluded in the grid of smaller pitch at the next iteration.

It is controlled at the following step 106 (i=V? s_(i)=S_(V)?) whether aprecision criterion is achieved. This criterion is defined by a number Vof iterations or a pitch S_(v) of the grid for which the obtained centerand radius are considered as being localized in a sufficiently accuratemanner.

If not (N), a new grid of reduced dimensions and of smaller pitch,centered on the region for which the strongest gradient variation hasbeen observed at the preceding iteration is redefined at step 107 (NEWGRID, i=i+1, s_(i)=s_(i+1)).

Generally, the process carries on until a maximum accuracy, that is, agrid having a pitch of one pixel, is reached, as illustrated in FIG. 2C.Such an accuracy enables exact determination of center C_(P) and radiusR_(P) of the pupil.

Once precision test 106 is positive (Y), the iris is localized at thenext step 108 (IRIS) by applying again a grid of possible centers todetermine with the integro-differential operators the iris radius R_(I)and, should the case arise, discriminate its center C_(I) from centerC_(P) of the pupil with a maximum reliability. The operators are hereapplied on arcs of a circle having diameters ranging from 100 to 180.Since the circles are approximately concentric, it is not necessary tostart again from a grid having the maximum pitch. A reduced number ofiterations (or even a single iteration) may be used by centering on thecenter of the pupil a grid sized according to the maximum(physiologically) possible interval between the two centers. Such acenter localization and radius determination of a second circle afterlocalizing a first circle is described in U.S. Pat. No. 5,291,560, whichis incorporated herein by reference.

The iris surface, that is, the ring-shaped surface between the pupillarycircle of center C_(P) and of radius R_(P) and the iridian circle ofcenter C_(I) and of radius R_(I), is then determined with a maximumaccuracy.

The surface thus obtained may be submitted to any appropriate digitalprocessing. In the considered example of an iris, it generally is aniridian recognition method based on the matching 109 (MATCHING) offeatures extracted from the obtained surface, for example, in one of theways described in above-mentioned U.S. Pat. No. 5,291,560 or inabove-mentioned U.S. Pat. No. 5,572,596, or in international patentapplication WO 00/62239, all of which are incorporated herein byreference.

Generally, the method described in relation with FIGS. 1 and 2 enableslocalizing at least one circle by exact determination of its radius andof the position of its center.

A major disadvantage of such a method is the successive repetition ofthe same operations on grids of decreasing size and pitch. This imposesa great amount of calculation. Further, for a given point, for example,point A of FIG. 2A close to the searched centers, the calculations arerepeated a great number of times. Accordingly, such a method has a slowimplementation.

Further, the various gradient variation comparison operations and thecorresponding calculations impose a relatively complex and bulkysoftware structure. Further, at each iteration, for each possiblecenter, the obtained data must be stored to be compared to thoseobtained for the other possible centers, to determine the region(s) ofstrongest gradient variation. This is necessary to recenter the nextgrid at step 107. Such a method thus requires using a significant memorysurface.

In a completely different field, to recognize the presence of a face ina digitized image, a method for determining the presence of a cornea orof an iris has been provided to identify the presence of an eye andcalculate a spacing between two eyes. This method consists of searchingconcentric geometric shapes by means of a Hough transform such asdescribed in U.S. Pat. No. 3,069,654. which is incorporated herein byreference. Such a method consists of considering, for the involvedgeometric shape (here, a circle), each pixel of the digitized image asbeing at the periphery of a circle of a given perimeter (radius), and ofapproximately localizing the center of this circle. For each possiblediameter of the searched circuit, an accumulator of same dimensions asthe image is associated with the digitized image. Each accumulatormemorizes, for a given radius, the number of times when a given point ofthe digitized image is determined as being the possible center of thesearched circle. This is performed by incrementing, for each radius, aninitially null weight assigned, in the accumulator linked to thisradius, to the position of the possible center in the image.

The searched center and radius are then obtained by determining, foreach considered radius, the point having the greatest weight and, forthe different considered radiuses, that for which the possible centerhas the maximum weight with respect to the other possible centersdetermined by the first determination. Such a method is described, forexample, in article “Detection of eye locations in unconstrained visualimages” by R. Kothari and J. L. Mitchell, published in Proc. ICIP'96,III pp. 519-523 (1996), or in article “Eye spacing measurement forfacial recognition” by M. Nixon, published in SPIE Proc., 575, pp.279-285 (1985), both of which are incorporated herein by reference.

Such a method has the disadvantage of being also long to execute.Further, for each pixel in the image, it imposes using a bulky memory,since, for each possible radius, an array having a number of lines andcolumns equal to the number of lines and columns of the digitized imagemust be memorized.

SUMMARY OF THE INVENTION

The present invention aims at providing a method for accurately locatingthe center of at least two concentric circles, which is faster thanknown methods.

The present invention also aims at providing such a method of which theimplementation requires a reduced memory space as compared to the spacerequired by the implementation of known methods.

The present invention also aims at providing such a method which alsoapplies to the localization of several circles, each of which isstrictly included in a circle of larger radius, but which are notconcentric.

The present invention also aims at providing a method for localizing aring included between two circles.

The present invention also aims at providing such a method which isapplicable to the localization of an iris of an eye in a digitizedimage.

To achieve these and other objects, the present invention provides amethod for localizing, in a digital image, at least two circles, one ofwhich is strictly included in the other by determination of theirradiuses and of the coordinates of their centers by means ofintegro-differential operators applied to at least one grid of possiblecenters, including the steps of:

evaluating an approximate position of the center of one of the twocircles; and

centering the grid in the vicinity of the approximate center, the gridbeing of reduced dimensions as compared to the image dimensions.

According to an embodiment of the present invention, the method uses asingle grid having a minimum pitch.

According to an embodiment of the present invention, the maximum size ofthe grid is smaller than the size of the larger circle.

According to an embodiment of the present invention, the maximum size ofthe grid is smaller than the size of that of the circles forming thelimit of strongest contrast.

According to an embodiment of the present invention, the maximum size ofthe grid is smaller than the size of the smaller circle.

According to an embodiment of the present invention, the step ofevaluation of the approximate position of the center includes the stepsof:

a) predefining a set of possible radiuses of the circle;

b) sizing two one-dimension accumulators in the form of a column arrayof at most the image size in abscissa and of a line array of at most theimage size in ordinate;

c) successively, for each image pixel:

-   -   i) successively selecting each possible radius;    -   ii) evaluating the position of the possible center of a circle        of the selected radius and the considered pixel of which is on        the periphery; and    -   iii) incrementing the accumulators at the abscissa and ordinate        of the possible center; and

d) selecting, as coordinates of the located center, the abscissa and theordinate corresponding to the maximum of the accumulators.

According to an embodiment of the present invention, the increment isone.

According to an embodiment of the present invention, the increment isweighted according to the significance of the gradient at the consideredpixel.

The present invention also provides a method for localizing, in adigital image, a ring defined by the inclusion of a first circle ofrelatively small radius in a second circle of relatively large radius,consisting of localizing the first and second circles according to themethod of any of the preceding embodiments.

According to an embodiment of the present invention, the ring is theiris of an eye, the first circle being the pupil of the eye and thesecond circle being the limit between the iris and the eye cornea.

According to an embodiment of the present invention, the pupil is thatof the circles of which the center is approximately searched.

The foregoing objects, features and advantages of the present invention,will be discussed in detail in the following non-limiting description ofspecific embodiments in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates in a flowchart the step sequence of a known iridianrecognition method;

FIGS. 2A to 2C schematically and partially illustrate the implementationof the method of FIG. 1;

FIG. 3 illustrates in a flowchart the step sequence of an iridianrecognition method according to an embodiment of the present invention;and

FIGS. 4A to 4D illustrate the implementation of the method of FIG. 3.

DETAILED DESCRIPTION

For clarity, the same elements have been designated with same referencesin the different drawings. Further, FIGS. 2A to 2C and 4A to 4D are notdrawn to scale.

A mode of iris recognition and location by determining the pupillary andiridian radiuses and by localizing the centers of the pupil and of aniris of an eye according to the present invention is described hereafterin relation with FIGS. 3 and 4A to 4D.

The method starts with a step 301 (ACQUIRING EYE IMAGE) of acquisitionof an eye image. Preferably, such an acquisition is performed so thatthe obtained image exhibits dimensions very close to the model, that is,a scale as close to one as possible. Such an acquisition may beperformed by means of an appropriate conventional biometry terminal, forexample, the device described in document EP-A-0,973,122, which isincorporated herein by reference.

FIG. 4A illustrates an image of an eye obtained by acquisition 301 by adigital CCD camera having a 580×760-pixel image, the eye being placed ata few centimeters only of the camera and being submitted to an infraredillumination. The obtained image includes a pupil P, an iris I, a cornealimited by a higher eyelid HE and a lower eyelid LE.

The method according to the present invention carries on with theapproximate localization of the eye center, that is, of the center ofthe pupil or of the iris. Preferably, the center of the circleexhibiting the strongest contrast is approximately located. As indicatedpreviously, in infrared illumination, the contrast is generally higherbetween the pupil and the iris than between the iris and the cornea.Preferably, the center of the pupil is thus first approximately located.The approximate localization enables determining an approximate centerwhich is, with respect to the real searched center, at a distance of atmost five pixels.

According to a first embodiment of the present invention, not shown, theapproximate center is determined by means of any known method. Forexample, one can use the method disclosed in the article “A new memorymodel for the parameter space in the Hough transform: Projection arrays”of M. H. Kim and H. Y. Hwang published in Proceedings TENCON 87, IEEEregion 10 conference “Computers and Communications Technology Toward2000”, Aug. 25-28, 1987, Volume 1, pages 222-226.

According to a preferred embodiment of the present invention, theapproximate center is determined by means of a method, an algorithm ofwhich is described hereafter in relation with FIG. 3.

As illustrated in block 302 (LOCATING IRIS) of FIG. 3, twoone-dimensional accumulators W_(x) and W_(y) are first generated. Thedimension of a first accumulator W_(x) is number N of lines of the imagebeing processed. The dimension of the second accumulator W_(y) is numberM of image columns. In a first sub-step 303, all current elements of thefirst and second accumulators W_(x)(i) where i varies from 1 to N, andW_(y)(j), where j varies from 1 to M, are set to zero.

The system is initialized to be placed at the first line (block 304,x=1), on the first column (block 305, y=1) and consider a first (block306, k=1) possible radius.

The localization is performed by successively implementing for each ofthe N lines x, for each point P_(xy) at the intersection of current linex and of a column y among the M columns, the following operations (block307):

-   -   calculating components Grad_(x) and Grad_(y) of the gradient of        current point P_(xy), that is, comparing the level of grey of        the current pixel with the levels of grey of the neighboring        points;    -   calculating abscissa x_(c) and ordinate y_(c) of center C of the        circle crossing current point P_(xy), to which the gradient        determined at the preceding step is tangent. Coordinates x_(c)        and y_(c) can be deduced, from components Grad_(x) and Grad_(y)        of the gradient and the equation of the circle of center C of        radius R_(k), as follows:

${{x_{c}\left( {x,R_{k}} \right)} = {x \pm \frac{R_{k}}{\sqrt{1 + \frac{{Grad}^{2}y}{{Grad}^{2}x}}}}};{{{and}\mspace{14mu}{y_{c}\left( {y,R_{k}} \right)}} = {y \pm {\frac{R_{k}}{\sqrt{1 + \frac{{Grad}^{2}x}{{Grad}^{2}y}}}.}}}$

The considered radius R_(k) is sampled from a set of K possible radiusesof the previously defined circle.

-   -   incrementing by one unit the first accumulator at position        W_(x)(i) corresponding to abscissa x_(c) of center C thus        calculated; and incrementing by one unit the second accumulator        at position W_(y)(j) corresponding to ordinate y_(c) of center C        thus calculated. As an alternative, the increment may be an        amount weighted according to the significance of the gradient at        the current point P_(xy) for which point C is the center of the        circle of radius R_(k) to which this gradient is tangent.

The successive operations of calculation of coordinates x_(c) and y_(C)are performed for each point P_(xy) for each of the K possible values ofradius R_(k), for example, for a pupil between 30 and 100 pixels.

For a considered point P_(xy), the only values to be stored are those ofcomponents Grad_(x) and Grad_(y) of the gradient and the content of thetwo accumulators W_(x) and W_(y). The two coordinates x_(c) and y_(c) ofcenter C, recalculated for each radius R_(k), need not be stored.

It is then successively controlled:

-   -   whether, for current point P_(xy), all K radiuses have been        processed (step 308, k=K?);    -   whether, for the considered line x, the M columns (or pixels)        have been scanned (step 309, y=M?); and    -   whether the last line N has been reached (step 310, x=N?).

As long as one of the preceding conditions 308, 309, 310 is notfulfilled (N), the corresponding counter of radius k is incremented(block 311, k=k+1), as well as the counter of column y (block 312,y=y+1) or of line x (block 313, x=x+1) and the appropriate sequence isresumed by returning either to the processing of the next radius byblock 307, or to the processing of the point of the next column, fromblock 306, or to the processing of the next line, from block 305.

As the calculations advance, the two components Grad_(x) and Grad_(y) ofthe gradient are recalculated for each current point P_(xy). Whenpassing to a next point, the values associated with the preceding pointare no longer necessary.

Thus, the same memory space can be used to store this parameternecessary to the K calculations of as many possible centers according toradiuses R_(k). The same minimum memory space can thus be assigned tothese buffer calculations for each change of current point. From onepoint to another, the only data to be kept are the contents of the twoaccumulators W_(x) and W_(y).

As illustrated in block 314, abscissa X0 of the approximate searchedcenter C0 is the value for which the corresponding term W_(x)(X0) of thefirst accumulator W_(x) is maximum. Similarly, ordinate Y0 of point C0is the point for which value W_(y)(j) is maximum:W _(x)(X0)=Max(i=1 . . . N)[W _(x)(i)], andW _(y)(Y0)=Max(j=1 . . . M)[W _(y)(j)].

Coordinates XO and Y0 of center C0 are accordingly obtained bydetermining, in each accumulator W_(x) and W_(y) the respective currentpositions i and j for which the respective values W_(x)(i) and W_(y)(j)are maximum.

FIG. 4B illustrates the result obtained at the end of step 314.

At the next step 315 (INTEGRO-DIFFERENTIAL OPERATORS AROUND (X0, Y0)),steps of searching the center and the radius of a circle are implementedbased on integro-differential operators applied on a gate G of pointsrepresenting possible centers. The searched circle is that of the pupil.As illustrated in FIG. 4C, grid G is, according to the presentinvention, of fine pitch (preferably, a minimum pitch, that is, 1 pixel)and is centered on previously-determined approximate center C0. Thisamounts to implementing steps 104 and 105 of the method of FIG. 1, butdirectly for final determination grid G. As an alternative, theexecution of a few loops of the method of FIG. 1 according to theapproximate center determination accuracy may be maintained. Grid Gbeing already centered on approximate center C0, the determination ofthe exact center C_(P) and radius R_(P) of the pupil is particularlyfast. Indeed, even if it is chosen to perform several runs, the numberof successive grids, and thus the amount of calculation, is reduced ascompared to the known method such as previously described. It should benoted that this exact determination of center C_(P) and of radius R_(P)of the pupil uses the same set of K possible values for the pupil radiusas that previously defined and used to determine approximate center C0.

Once center C_(P) and radius R_(P) of the pupil have been determined,integro-differential operators are applied again on circles having theirradiuses in a possible range of the average diameter of the iris of aneye to determine (block 316 (IRIS CENTER & BOUNDARIES) of FIG. 3; FIG.4D) radius R_(I) and center C_(I) of the iris. As for the pupil, thisdetermination preferentially uses a single grid with a minimum pitch.This grid is centered on center C_(P) and its dimensions are a functionof the maximum possible distance between centers C_(P) and C_(I), sothat it necessarily includes center C_(I).

The ring forming the eye iris has thus been precisely located. It canthen be submitted to any appropriate processing, for example, arecognition processing by being compared to the content of a database(block 317, MATCHING).

The general time of localization of the ring forming the iris isconsiderably reduced as compared to conventional methods implementingfor the entire image a series of successive grids of possible centers ofdecreasing dimensions and pitches. Further, the precision of thislocalization is maximum.

The iris localization method described in relation with FIGS. 3 and 4generally enables locating by determination of its center and of itsradiuses any elliptic geometric shape. In the very example of thelocating of an iris, instead of considering the pupil and/or the iris asa perfect circle, these may be considered as having an elliptic shape,either upon determination of the approximate center—steps 303 to 314 ofFIG. 3—or upon application 315 of the integro-differential operatorswhich are then applied on arcs of an ellipse instead of on arcs of acircle.

Generally, the method according to the present invention applies to thelocating by determination of their centers and radiuses of any number ofelliptic geometric shapes, each geometric shape being strictly includedin a geometric shape of greater perimeter, except for that having thegreatest dimensions. Further, the searched elliptic shapes areconcentric or slightly off-centered.

This localization method may be used to locate at least one ringincluded between at least two of the located geometric shapes. Forexample, in the wood working industry, it enables detecting the presenceof knots in the wood in quality control tests. It is then alsoadvantageously possible to measure their size, which enables determiningtheir impact on the solidity of the final product.

In the previously-described iris localization application, thelocalization is previous to an iridian recognition usable as arecognition parameter to identify an individual. An example ofapplication is the access control: access to a physical site, such as acontrol of the opening of a door with a code, or with an access card;access to a bank account usually protected with a password; access toany device such as a computer or a mobile phone usually protected by acode to be typed. Such a device may also replace the fingerprintidentification or another biometric identification.

Of course, the present invention is likely to have various alterations,modifications, and improvement which will readily occur to those skilledin the art. In particular, it has been considered in FIG. 4 that themethod starts with the acquisition of an eye image. However, it maystart with the access in a database to a previously-digitized image.This image may then come from a distant database. In FIG. 4C, it hasbeen assumed that center C_(P) differs from approximate center C0.However, approximate center C0 could appear to be the searched center ofthe pupil. In the approximate center search algorithm, the image hasbeen assumed to be scanned line by line. It should be clear to thoseskilled in the art that any other type of scanning, for example, columnby column, would also be possible. Further, the loop control mode (linecounter x, column counter y, radius counter k) may be modified in anyappropriate manner. Moreover, instead of searching the center of thepupil as the approximate center, that of the iris could be searched,provided to appropriately modify the predefined set of possible valuesfor the radius.

Further, the circle forming the limit with the strongest contrast, thatis, that having the points with the highest gradient values, hasapproximately been located among searched circles of various possibleradiuses. It would however be possible to attempt to determine theapproximate center of another circle of lower contrast, for example, ifsaid circle has a particularly reduced number of possible radiuses.

Such alterations, modifications, and improvements are intended to bepart of this disclosure, and are intended to be within the spirit andthe scope of the present invention. Accordingly, the foregoingdescription is by way of example only and is not intended to belimiting. The present invention is limited only as defined in thefollowing claims and the equivalents thereto.

1. A method for localizing, in a digital image, at least two circles,one of which is entirely included in the other, the method comprising:estimating a position of a center of one of the two circles; centering agrid in a vicinity of the estimated position of the center, the gridbeing of reduced dimensions as compared to the image dimensions;determining a first radius and first coordinates of the center of theone of the two circles; determining a second radius and secondcoordinates of the center of another of the two circles based at leastin part on the first radius and/or first coordinates of the center ofthe one of the two circles; and outputting an indication of thelocalization of the at least two circles.
 2. The method of claim 1,using a single grid having a minimum pitch.
 3. The method of claim 2,wherein one of the two circles is larger than another of the twocircles, and wherein the maximum size of the grid is smaller than a sizeof the larger circle.
 4. The method of claim 3, wherein the maximum sizeof the grid is smaller than a size of the circle forming the limit ofstrongest contrast.
 5. The method of claim 3, wherein the maximum sizeof the grid is smaller than a size of the smaller circle.
 6. The methodof claim 1, wherein the step of estimating the position of the centerincludes: a) predefining a set of possible radiuses of the one of thetwo circles; b) sizing two one-dimension accumulators in a form of acolumn array of at most a size of an image in abscissa and of a linearray of at most the image size in ordinate; c) successively, for eachimage pixel: (i) successively selecting each possible radius; (ii)evaluating the position of a possible center of a circle of the selectedradius and a considered pixel of which is on the periphery; and (iii)incrementing the accumulators at the abscissa and ordinate of thepossible center; and d) selecting, as coordinates of the located center,the abscissa and the ordinate corresponding to the maximum of theaccumulators.
 7. The method of claim 6, wherein incrementing theaccumulators includes changing the accumulators by an increment of one.8. The method of claim 6, wherein incrementing the accumulators includeschanging the accumulators by an increment which is weighted according tothe significance of the gradient at the considered pixel.
 9. A methodfor localizing, in a digital image, a ring defined by the inclusion of afirst circle of relatively small radius in a second circle of relativelylarge radius, consisting of localizing the first and second circlesaccording to the method of claim
 1. 10. The method of claim 9, whereinthe ring represents an iris of an eye, the first center represents apupil of the eye and the second circle represents a limit between theiris and a cornea of the eye.
 11. The method of claim 10, wherein thepupil is the one of two circles.
 12. A method of determining a positionof a center of a circle in an image, the method comprising: estimating aposition of a center of a circle in an image, the image having an imagearea; centering a grid around the estimated position of the center, thegrid having a grid area that is less than the image area determining theactual position of the center of the circle within the grid; andproviding an indication of the actual position of the center of thecircle.
 13. The method of claim 12, wherein the circle has a circle areaand the circle area is smaller than the image area and is larger thanthe grid area.
 14. The method of claim 12, further comprisingdetermining an actual radius of the circle.
 15. The method of claim 12,wherein said step of estimating a position of a center of a circleincludes: a) determining a set of possible radiuses; b) determining afirst one-dimension accumulator representing at most the number of linesof the image and a second one-dimension accumulator representing at mostthe number of columns of the image; c) selecting one radius from the setof possible radiuses; d) determining a gradient of a possible center ofthe circle; e) incrementing the first and second accumulators at thepossible center; f) repeating steps c, d and e for each radius of theset of possible radiuses; g) repeating steps c, d, e and f for eachpossible center of the circle; and h) determining that the estimatedposition of the center of the circle is where the first and secondaccumulators are at a maximum.
 16. The method of claim 15, wherein saidstep of determining a gradient of a possible center of the circleincludes comparing a first level of gray of the possible center with asecond level of gray of a neighboring point.
 17. A method of determiningpositions of centers of first and second circles in an image, the methodcomprising: estimating a position of a center of a first circle in animage, the image having an image area; centering a first grid around theestimated position of the center, the first grid having a first gridarea that is less than the image area; determining the actual positionof the center of the first circle within the first grid; centering asecond grid around the actual position of the center of the firstcircle, the second grid having a second grid area that is less than theimage area; determining the actual position of the center of the secondcircle within the second grid; and outputting an indication of thepositions of centers of the first and second circles in the image. 18.The method of claim 17, wherein the first circle is smaller than thesecond circle.
 19. The method of claim 18, wherein the first circle islocated within the second circle.